Note on Moufang-Noether currents

TL;DR

This paper constructs derivative Noether currents from Moufang transformations, analyzes their commutators, and reveals that the resulting charge algebra forms a birepresentation of the tangent Mal'cev algebra of an analytic Moufang loop.

Contribution

It introduces a novel connection between Noether currents and Moufang loop structures, specifically linking charge algebra to Mal'cev algebra representations.

Findings

Derived Noether currents for Moufang transformations.

Found equal-time commutators of these currents.

Charge algebra is a birepresentation of the tangent Mal'cev algebra.

Abstract

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.